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Open Accumulator Isothermal Compressed AirEnergy Storage (OA-ICAES) System

Perry Y. Li, Eric Loth, Chao (Chris) Qin, Terrence W. Simon and James D. Van de Ven

Abstract

Cost-effective, scalable and dispatchable energy storage systems is the key to integrating unpredictable andintermittent green energy, such as wind and solar energy, into the electrical grid. This chapter describes a novelOpen Accumulator Isothermal Compressed Air Energy Storage (OA-ICAES) system for wind turbines that storesexcess energy in the form of high pressure (210 bar) compressed air before conversion to electricity. The stored energyis then used to generate electricity when demand exceeds supply. The Open Accumulator architecture increases thesystem’s energy density, whereas the isothermal compressor/expander increases the efficiency and power-density.They result in an efficient, cost-effective, hydrocarbon fuel-free energy storage system not restricted by geographicfeatures to replace today’s natural gas “peaker” plants. Since the system can turn on/off within a second, it canstore and dispatch power rapidly on demand and can be used for frequency regulation. Because storage is prior toconversion to electricity, downstream electrical components (e.g. generator, transmission and interconnects) can bedownsized for mean power instead of peak power.

To realize isothermal compression/expansion, a liquid piston with porous media inserts, optimized trajectory andchamber designs, efficient power take-off, and water droplet sprays, are used. Plant and supervisory levels controlsystems coordinate and optimize the system performance.

Keywords: Compressed air energy storage, isothermal compression/expansion, open accumulator, liquid piston,porous media, optimal trajectories, spray cooling, variable linkage pump/motors, supervisory control, maximumenergy capture, revenue maximization.

I. INTRODUCTION

Despite their abundance, fossil fuels, such as coal, oil and natural gas, will produce green house gases and willexacerbate the state of global warming and climate change. Displacing fossil fuels by clean and renewable energy isnecessary to reverse this trend. Although renewable resources such as wind or solar energy are quite abundant, theyhave a significant drawback - they are not available on-demand and their availabilities are often unpredictable. Forexample, wind speed varies from hour to hour and from day to day with higher intensity wind usually occurring atnight; solar energy is available only during the day and when clouds are not in the way. There is often a mismatchbetween when these renewable energies are available and when demand is high.

The variable and stochastic nature of these renewable energies pose a significant challenge in incorporating largeamount of these resources into the electrical grid. The challenge lies in that when the renewable resources becomeunavailable, other energy resources that can be called upon quickly are needed. Currently, natural gas power plants,with sufficient capacity to compensate for variability of the renewables, are used for this purpose. Besides having acarbon dioxide (a green house gas) footprint, these natural gas “peaker” plants are expensive to build, maintain andoperate. Their use increases the overall cost and diminishes the environment benefits of renewable energies. To anextent, a smart electrical grid that connects a broad portfolio of generators and demands across a wide geographicdomain can mitigate the needs for “peaker” plants by compensating for the variability, provided that adequatetransmission capacity and a responsive market exist. Alternatively, energy storage can be used in conjunction withwind and solar to store excess energy that is to be re-generated when demand is high. This allows renewableenergies to be predictable and available on-demand, eliminating the need for “peaker” plants.

We focus now on wind energy. If an energy storage system is configured to store energy locally at the windturbine/wind farm, and prior to generating electricity, the electrical components, including the generator, power

P. Y. Li is the corresponding author. P. Y. Li, T. W. Simon and J. D. Van de Ven are with the Department of Mechanical Engineering,University of Minnesota, Minneapolis, MN 55455. Q. Chao and E. Loth are with the Department of Mechanical and Aerospace Engineering,University of Virginia, Charlottesville, VA 22904. Emails: perry-li@umn.edu, q4jn@virginia.edu, loth@virginia.edu,simon002@umn.edu, vandeven@umn.edu

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electronics and interconnects, can be downsized for the mean power instead of the peak power. This is significantsince the capacity factor of a typical zone six wind turbine is only 47% [1] (with many other turbines having acapacity factor below 40%), meaning that downsizing by 50% is possible. The savings in capital expense (CAPEX)is even more significant for off-shore wind installations since electrical collection and transmission cost are fourtimes the cost of on-shore deployment, accounting for 15% of the total cost (versus 6% for on-shore). The costsaving for off-shore collection and transmission alone would be 20% [2], [3]. Since energy price can vary by anorder of magnitude during a hot summer day, it is much more useful (and profitable) to generate electricity accordingto demand rather than according to wind availability, as is currently practiced. The amount of wind energy that canbe captured will also be increased as it is no longer necessary to reserve for control, through curtailment, a portion(typically 5%) of the available power. The cut-off wind speed (to protect the turbine) for maximum power trackingcan also be increased to the limit of the mechanical structure or of the Power-Take-Off (PTO), instead of that ofthe electrical generator.

Storing the electrical energy locally in batteries is an option, except for the cost, need for AC/DC/AC conver-sion, low power density, weight, limitation in charge/discharge cycles, end-of-life environmental impact, and lowefficiency in cold climates. Also the wind turbines would require a full sized generator and power electronics toaccommodate the available power. Pumped Hydro Storage (PHS) and conventional Compressed Air Energy Storage(CAES) systems are economical utility-scale methods (several times less expensive than batteries [4]) but sincethey require a large reservoir or an underground cavern, they depend greatly on geographies. Existing conventionalCAES systems, such as the plants in McIntosh, USA or Huntdorf, Germany, use excess electricity to compress air(up to 80 bar [8MPa] ) into a cavern, and the energy is recuperated by burning a mixture of the natural gas with thecompressed air. The requirement for additional hydrocarbon fuel and the low efficiency of the storage-regnerationcycle itself (estimated at 29-36% [5]) diminish the attractiveness of the conventional CAES processes.

Compressed air energy storage (CAES) has competitive energy density and power density, especially if operatedat high pressure. If the compressed air pressure is raised to 350 bar (35MPa), the energy is compressed andextracted in a near-isothermal manner, and if the open accumulator architecture (see below) is used, as much as170MJ (47kWh) can be stored per m3 of volume. For a PHS to achieve an equivalent energy density, the reservoirwould need a 17km elevation! Gases at 350 bar (35MPa), and even higher, pressures are routinely stored in steelor composite hydraulic accumulators and scuba tanks. It is expected that with larger vessels, improved designs andeconomy of scale, the storage vessels can be quite cost-effective. Use of engineered pressure vessels allows CAESto be sited anywhere without geological constraints. To store an average power of 3MW (for a peak 5MW turbine)continuously for 8 hours, a volume of 500m3 is needed. Such a vessel is compatible with a turbine of this scale(⇠ 100m tall and a blade span of 60m). The storage vessel can even be integrated into the structure of the turbinetower, or used as ballast.

In this chapter, we describe research for a novel Compressed Air Energy Storage (CAES) concept for windturbines (or other renewable energy sources with mechanical output) that was first proposed in [6], [7] for storingenergy locally prior to electricity generation. In this system (Fig. 1), compressed air is stored in high pressure(⇠ 200� 350bar [20-35MPa] ) vessels; the compressor/expander used to store and extract energy operates nearlyisothermally so that it is efficient; and a variable hydraulic drive, instead of a mechanical gearbox, is used for powertransmission. This improves the reliability of the transmission system and allows the generator and storage systemto be housed down-tower, thus reducing construction and repair costs. In addition, a cost effective, fixed-speedinduction generator can be used instead of the combination of a permanent magnet synchronous generator andpower electronics for frequency and voltage conversion. Since the system can be turned on and off in less than0.1s, it can be used to provide the lucrative ancillary services such as grid frequency regulation. It is well suited forthis application because of its cost effectiveness for utility scaled deployment. Current (circa 2015) target storageand capacity costs are in the order of $150/(kWh) and $1000/(kW ) respectively.

The two major challenges for realizing this concept are: 1) the compressor/expanders are generally not veryefficient or powerful; 2) the pressure in the storage vessel reduces as compressed air in the storage vessel depletes,making it difficult for the air compressor/expander to maintain either its efficiency or power at all energy levels. Thefirst challenge is overcome by developing a near-isothermal air compressor/expander with enhanced heat transfer.This is achieved using a liquid piston compressor/expander [8] in conjunction with porous media inserts [9] andinjected droplet sprays [10]. The latter challenge, which leads to low energy density (hence requiring large storagevessels), is overcome by deploying the open accumulator configuration with a dual-chamber storage vessel for

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Water reservoir

Hydraulic pump - B

Hydraulicpump/motor C

Liquid pistonIsothermal air compressor/expander D

EAir

Liquid

Liquid pistonpump/motor

Liquid pistonwater supply

Generator F

Fig. 1. Open Accumulator Isothermal Compressed Air Energy Storage System (OA-ICAES) for wind tubine

both liquid and compressed air, such that energy can be stored/retrieved hydraulically and pneumatically [11]. Bycoordinating the hydraulic and pneumatic paths, the pressure can be maintained regardless of the energy content.Because hydraulic components are more power-dense, and can be turned on/off quickly, they can be used for peaktransient power while the air compressor/expander can be downsized for steady power. An appropriate controllerthat coordinates these two power paths is essential for the simultaneous pressure regulation, tracking of the desiredgenerator power, and maximizing wind power capture in the presence of supply or demand power variations. Theefficiency and performance of the CAES system would depend significantly on the design of the controller.

The rest of this chapter is organized as follows. Section II describes the overall system architecture. Section IIIpresents the liquid piston isothermal compressor/expander. Section IV describes the spray cooling concept. SectionV summarizes the control system concepts. Section VII contains discussion and concluding remarks.

II. OPEN ACCUMULATOR ISOTHERMAL COMPRESSED AIR ENERGY STORAGE (OA-ICAES) SYSTEMARCHITECTURE

The proposed CAES with the open accumulator architecture [11] is shown in Fig. 1. A variable displacementhydraulic pump (B) attached to the wind turbine rotor (A) in the nacelle converts wind power to hydraulicpower. At down-tower, a variable displacement hydraulic pump/motor (C), a near-isothermal liquid piston aircompressor/expander (D) and a fixed speed induction generator (F) are connected in tandem on a common shaft.They are powered by the pump (B) and exchange power with the storage vessel (E) with both liquid and compressedair at the same pressure. This allows energy to be stored in or extracted from (E) either hydraulically (as in aconventional hydraulic accumulator) or pneumatically (as in a conventional air receiver). In both cases, energy isstored in the compressed air. By coordinating the hydraulic and the pneumatic power paths, the pressure in thestorage vessel (E) can be controlled independent of the energy content, unlike a conventional closed hydraulicaccumulator with only a hydraulic port or a compressed air receiver with only a pneumatic port. For example,as compressed air is being released from (E), some liquid can be added to reduce the compressed air volume to

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maintain the pressure. The hydraulic fluid is preferably water for cost and environmental reasons so the hydrauliccomponents (B,C,E) should also be compatible with water.

In conventional CAES systems, such as the ones in McIntosh, AL, USA or in Huntorf, Germany, the storagevolume contains compressed air only, typically up to 70-80 bar (7-8 MPa). Pressure varies greatly as energyis stored or depleted. When the pressure is low, greater airflow is needed for the same power. This limits thecompressor/expander power, or makes the low-pressure compressed air unusable. The large pressure variation alsomakes it difficult to optimize components to operate efficiently throughout the pressure range. For this reason, theMcIntosh CAES plant limits pressure within a 50-78 bar (5-7.8MPa) range. Since the compressed air that remainsat the lower pressure is not used, the energy density is low 1 (16.5 MJm

�3 or 4.6 kWhm

�3). If the remainingcompressed air at 50 bar (5MPa) is allowed to expand to ambient pressure, the energy density can be increased by65%.

In the open-accumulator concept [11], the storage vessel holds both liquid and air. Notice from Fig. 1 that energycan be added/subtracted to/from the storage vessel pneumatically via the compressor/expander or hydraulically viathe hydraulic pump/motors. The hydraulic power path stores energy by compressing the air already in the vessel withthe addition of liquid similar to a hydraulic accumulator. This path is power-dense, but the amount of energy thatcan be stored this way is relatively low as the maximum pressure limit is reached quickly. It is well suited for highpower transient events such as wind gusts or periods of sudden generation power demand. The pneumatic powerpath stores energy by putting more compressed air into the vessel. This path is energy-dense, but the power densityis much lower than the hydraulic path, so it is more suited for steady power. The hydraulic path is 20-30 timesmore power-dense than the pneumatic power path, whereas the pneumatic path is ⇠ 20 times more energy-densethan the hydraulic path [11]. This dual power path property offers several benefits:

1) Increase energy density: By controlling the liquid volume, pressure can be maintained regardless of theamount of compressed air stored. This makes all the compressed air usable at the system’s nominal pressure,thus realizing the full energy capacity. At 210 bar (21MPa), the energy density is 91.4MJm

�3 (25.4kWhm

�3),a 5.5-fold increase. This increase makes it economically feasible to use pressure vessels instead of undergroundcaverns to store the compressed air in grid-scale applications.

2) Downsizing compressor/expander: Since hydraulic pump/motors are cheaper and more compact than simi-larly powered pneumatic compressor/expanders, one can reduce cost and size by utilizing the hydraulic powerpath for large transient peaks (e.g. from wind gust) and downsizing the air compressor/expander for steadypower.

3) Optimizing efficiency: With pressure maintained in a narrow range, components need only be optimizedover this range. Furthermore, the redundancy afforded by the dual power path provides an extra degree offreedom to optimize system efficiency while storing/releasing the desired amount of energy and maintainingpressure within a reasonable range. Simulation (see section V) shows that an efficiency increase of 4% ispossible.

4) Rapid response: Hydraulic actuation can usually be achieved in 10-100ms. This allows the storage systemto respond rapidly to sudden changes in power input or power demand. This rapid response can be utilizedto provide ancillary services for the electrical grid, such as frequency regulation or grid stabilization.

The near-isothermal liquid piston air compressor/expander is a critical component of the system as it is responsiblefor transforming mechanical energy into stored energy, and vice versa. Thus, for the system to be economical, itmust be both efficient and power-dense. Sections III-IV will describe the various techniques being used to achievethese characteristics.

III. LIQUID PISTON ISOTHERMAL COMPRESSOR/EXPANDER (C/E)Making the air compressor/expander efficient and power-dense is challenging because of thermal effects. For

example, if compression/expansion by 350-fold were done isentropically, the result would be extreme temperaturevariations about the ambient temperature (+1200K/-250K), which the materials cannot normally tolerate. Even ifthis is possible, the compressed air, which has been heated during compression, is expected to stay within thestorage vessel for hours before reuse. During this time, it will cool to the ambient temperature. Figure 2 illustrates

1assuming energy is extracted isothermally.

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Fig. 2. Pressure-volume plot illustrating work input (Win

) and output (Wout

). The compressed air is assumed, conservatively, to return toambient temperature inside the storage.

the relationship between the pressure-volume curve and the work input and output. The work input W

in

is thearea under the P-V curve above the initial pressure P0 for compression from P0 to rP0, including the isobaricejection of the compressed air into the reservoir at rP0. The output work is the area under the expansion P-Vcurve from rP0 to P0 including the initial isobaric charging at rP0. To be efficient, both the compression andexpansion P-V curves must be close to each other. They must also be close to the isothermal P-V curve at ambienttemperature T0 if the heat sink and source are also at T0. Conventionally, a high pressure gas compressor/expanderconsists of multiple stages with inter-cooling/warming. This creates a zig-zag pressure-volume curve consistingof successive adiabatic compression/expansion and constant volume cooling/warming segments. As the number ofstages increases, compression and expansion approach the most efficient isothermal processes, at the temperatureof the environment.

The minimum amount of work input and the maximum amount of work output are, therefore, the input work oroutput work when the process is isothermal at the ambient temperature. We refer to this as the storage energy:

E

store

:= W

in

(⇣iso

) = W

out

(⇣iso

) (1)

where ⇣

iso

denotes the isothermal process. The input and output efficiencies are defined as:

⌘

in

:=E

store

W

in

; ⌘

out

:=W

out

E

store

(2)

Since, from the first law of thermodynamics,

dE = �PdV +Qdt

where E(P, V ) is the internal energy of the air being compressed/expanded, �PdV is the differential compressionwork, Q(h,A,�T ) is the heat transfer (rate) which is a function of the heat transfer coefficient h, the heat transferarea A and the temperature difference between the air and the heat transfer surfaces �T , the time it takes to tracea pressure-volume (P-V) curve is given by:

t =Z

⇣eject/charge

dt =Z

dE(P, V ) + PdV

Q(h,A,�T )(3)

The integration is taken over the path of the compression/expansion process. From this, we see that the input andoutput powers, defined as:

Power

in

:=E

store

t

c

; Power

out

:=W

out

t

e

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Fig. 3. Schematic of a near-isothermal liquid piston compressor/expander.

(tc

, te

are the times for the compression and expansion processes) are inversely proportional to process time anddepend on the heat transfer rate Q in the compressor/expander, or in the inter-cooling/warming processes. Notethat the P � V curves determine the efficiency of the process and the heat that must be transferred. A P-V curvethat requires less heat to be transferred (and hence less time) tends to deviate more and more from the isothermalcurve and the process becomes less and less efficient. Hence, there is an inherent trade-off between efficiency andpower of a compressor/expander. For this reason, typical pneumatic compressors are either inefficient, low poweror both.

To mitigate this trade-off in order to increase both efficiency and power density, the air compressor/expander isenhanced with heat transfer using a liquid piston concept [8]. A schematic is shown in Fig. 3 which consists of anair compression/expansion chamber filled with porous media and a hydraulic pump/motor used to actuate a liquidpiston. The porous material is used to increase the heat transfer surface area [8], [9], [12]. A liquid (water) pistoncan flow through the porous material, provides a tight seal for the compressed air and serves as a heat sink andheat source for the porous media. The liquid piston is also advantageous in displacing and ejecting compressed air,eliminating dead-volumes that decrease system efficiency. The liquid piston pump/motor, which pumps water intothe chamber during compression and receives water during expansion, serves as the power-take-off (PTO) interfacebetween the compression/expansion process and the mechanical domain.

When storing energy pneumatically, the liquid piston pump/motor pumps water into the compression/expansionchamber, compressing the air within it. Thermal energy of compression is transferred to the porous material and tothe water to maintain a near-isothermal operation. When the chamber pressure exceeds that of the storage vessel, avalve is opened and the compressed air is ejected and stored in the pressure vessel. The chamber is then refreshed byreleasing the water and filling it with atmospheric air for the next cycle. When discharging energy, the compressedair is initially released into the expansion chamber. The valve is then closed. As the air expands, the liquid pistonretreats, the liquid piston pump/motor is motored and work is derived. Thermal energy is supplied from the porousmaterial to maintain the temperature of the expanding air.

Section III-A will discuss the porous media modeling and design. Section III-B presents how compressor/expanderperformance is enhanced by optimizing the motion trajectory of the liquid piston, porous media distribution andchamber shape [13], [14], [15], [16] (see section III-B). Section III-C presents a new efficient liquid pistonpump/motor design. Section IV describes how tiny water droplets [10], [17] enhance heat transfer in this application.

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Fig. 4. Two styles of porous media heat exchangers: honeycomb and open cell foam.

Fig. 5. Interrupted plate heat exchanger fabricated using ABS plastic or metal powder by 3-D printing. [24], [18]

A. Porous media heat exchanger modeling and design

Effective regenerative heat exchangers require close thermal communication between the heat exchanger and theair being compressed and expanded. This requires 1) a large surface area per unit volume to effect that heat transferwith a small temperature difference, 2) maintaining a temperature difference as heat transfer proceeds, 3) a heatexchange material that has a high thermal capacity relative to that of air. In addition, a low pressure drop is alsodesirable. Heat exchanger geometries that offer large ratios of heat transfer area to volume include beds of beads,honeycombs, a series of parallel small tubes, screens or fiber beds, open cell foams and parallel plates.

Figure 4 shows two styles of heat exchangers: honeycomb and open-cell foam. Honeycomb regenerators thathave short flow-direction sections to allow some mixing between layers and reinitiation of thermal boundary layersat the beginning of each segment are more effective. Open-cell foams tend to have higher pressure drop than thehoneycomb, but offers good lateral mixing. They also are more inclined to trap the air or water as the interfacebetween the two passes through the matrix. A geometry that our group has found most effective is the interruptedplate regenerator, such as shown in Fig. 5. It has the repeating thermal boundary layer feature, offers effectivemixing between plate layers and, if important, allows effective draining of liquid and minimal trapping of gas whenliquid is present. The interrupted plate regenerator matrices with multiple layers can be fabricated with 3-D printingusing ABS plastic or metal powder [18], [19].

To analyze the effectiveness of the heat exchanger regenerator matrix that consists of a matrix of solid webs withair in the interstitial spaces, a porous medium modeling approach is used. Modeling is done by averaging over thefine features of the flow using such terms as porosity (the interstitial volume as a fraction of the total volume),permeability and inertial coefficients (for computing the losses due to flow forces within the porous region). Porositycan be determined by the geometry of the medium, permeability and inertial coefficients are either measured orcomputed via detailed flow calculation on a segment of the porous medium, called the Representative ElementaryVolume (REV). One thermal equation is needed for the solid region and one for the air region. They also areaveraged over the REV. Modeling of the processes within the REV involves determining the heat transfer betweenthe solid and the air using the area per unit volume and a heat transfer coefficient per unit volume, h

v

. The area iscomputed from the geometry and h

v

is determined by measurement or by detailed computation within the REV.

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Fig. 6. Temperature and wall heat flux in a unit cell (REV) of an interrupted plate heat exchanger (from [18] [19]).

Important to the CAES analysis is the compression work in the air energy equation. Dissipation is usually toosmall to include. Conduction within the air and within the solid are computed with models from the literatureor are measured or computed in the REV calculations. They are usually not very important terms relative to theterms for heat transfer between air and solid. If eddies are present in the interstitial spaces, mixing (transport) bydispersion is included. Modeling terms for dispersion can be measured or computed in the REV calculations. Withthese modeling parameters, the flow and temperature fields, averaged over the pore regions, can be computed. Theoverall porous medium model is then used to compute the air temperature and pressure rises due to compressionand the thermal energy storage in the solid part of the porous material. Once developed, the models are used todetermine the performance of the regenerator, as affected by 1) material, 2) geometry, 3) how the porous mediumis distributed within the compression space [20], [21]; 4) the shape of the compressor vessel and 5) the pumpedflow rate vs. time during compression [22], [15], [23]; and generally, the design and operation of the compressor.

Figure 6 shows the REV geometry used to compute the pore-scale flow and heat transfer modeling terms as wellas the flow and solid temperature fields. Modeling terms are extracted for use in the porous medium model. Anexample is the heat transfer coefficient in Fig. 7 for various conditions. It is developed from many REV simulations.One can see in these heat transfer coefficient results a transition, with increasing Reynolds number, from laminar-like flow to turbulent-like flow. Also computed from the REV simulations are models for pressure drop, dispersionand dissipation to be used in the porous medium model. A comparison of computed efficiencies for the plasticand metal interrupted-plate and honeycomb regenerators is given in [24]. When there is no porous medium inthe compressor, strong 3-D flow features develop, as computed by 3-D analysis [25]. The heat exchange matrixsuppresses the motion of these 3-D flow features.

Recently, it was discovered that matrices with plates that are not aligned with the flow but are at an angle of attackgive increased heat transfer coefficients with only minor pressure loss penalties. This suggests that a tilted-matrix,interrupted-plate design as shown in Figs. 8 will increase heat exchanger performance [26].

Verification of the computed values is essential. In the case of the interrupted plate heat exchanger, computationwith the REV model is generally reliable, though such features as flow instabilities leading to mixing and transitionto turbulence may not be accurately computed. But in more complex geometries, like bead beds or open-cell porousfoams [27], the REV computations are not so reliable, in isolation, and experiments for verification are needed.Detailed data for pore-level processes, like heat transfer coefficients, are difficult to extract but comparisons of gasspace volume and bulk temperatures during compression, measured and computed, can be made. Figure 9 showssuch a comparison.

The efficacy of using a liquid piston with porous media to improve efficiency/power density trade-off has beendemonstrated in both low-pressure (1-10 bar [0.1-1MPa] ) and high-pressure (7-210 bar [0.7-21MPa]) compressionand expansion in bench top experiments [12], [28]. With constant velocity compression/expansion profiles, addingan interrupted plate (2.5mm plate distance) heat exchanger (Fig. 6) uniformly in space leads to an over 10 timesincrease in power density at 90% efficiency (Fig. 10). The increase means that for the same power capability, thecompressor/expander size can be made one-tenth the original size (and proportionately cheaper). It was confirmed,as hypothesized, that the increase in heat transfer area is the dominant contributor to the improvement. A study

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Fig. 7. Dimensionless volume heat transfer coefficient (Nusselt number) NuV

= hav

L2/k vs. Reynolds number for the interrupted plateheat exchanger. The different points represent different geometries, as given by different l values (from [18])

Fig. 8. Tilted matrix interrupted plate heat exchanger.

Fig. 9. Comparison of measured and experimental (from a zero-D model) temperatures. Dimensionless temperature: T/Tinit

; dimensionlessair volume: V/V

init

(from [18])

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Fig. 10. Efficiency versus power-density with and without porous media. Top: Compression; Bottom: Expansion. A, B, C, D, E indicatedifferent porous medium distributions (from [12]).

of the placement of the porous medium in the chamber revealed that the porous media is most useful when it isat the top of the chamber where the high pressure air resides. This suggests that, with a given amount of porousmedium solid volume, its distribution in the chamber can have an important effect on performance and should beoptimized (see section III-B).

B. Optimization of compression/expansion trajectory, porous medium distribution and chamber shape

As shown in Fig. 2, the choice of the P-V curve determines the work and efficiency of the process. Given heattransfer coefficient (h) and surface area (A), this choice also determines the process time and hence, power. Ithas been shown through theoretical [13], [14] and numerical [15] analyses as well as in experiments [22], [29],that an optimal P-V curve can significantly increase power density for the same efficiency (3-5 times improvementover linear or sinusoidal trajectories). A computationally efficient method has been developed using DynamicProgramming to determine the solution to this Pareto optimal control problem under general constraints and heat

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TABLE IEFFECT OF OPTIMIZATION OF POROSITY DISTRIBUTION, CHAMBER SHAPE AND COMPRESSION TRAJECTORY (FROM [16])

Cases Porosity Flow Rate Shape Efficiency Compression Time Power Density1 uniform constant (43cc/s) uniform 92% 33s 71.2 kW/m3

2 uniform optimal uniform 92% 10.8s 217.3 kW/m3

3 optimal constant (149cc/s) uniform 92% 9.6s 245.6 kW/m3

4 optimal optimal uniform 92% 3.5s 669.3 kW/m3

5 optimal optimal optimal 92% 1.6s 1470 kW/m3

Fig. 11. Sample optimal compression (liquid piston flow rate) trajectory, porous media distribution and compression chamber shape. Bluecolor indicates porous media; yellow indicates empty.

transfer correlations [16]. The optimal compression/expansion process typically consists of a sequence of fast-slow-fast segments. In the simple case when the product hA of the heat transfer coefficient, h, and surface area, A, isa constant and there is no constraint on the piston speed, the optimal trajectory consists of an adiabatic segment(infinitely fast), an isothermal segment at an elevated temperature (slow), followed by a final adiabatic segement(fast).

The compression/expansion trajectory has also been optimized in combination with the distribution of the porousmedia, and the shape of the compression/expansion chamber [16]. Here, the total porosity of the porous media isgiven but how it is distributed is optimized. The chamber shape is optimized with the constraint on the volume andthe maximum length. Table I shows that the power density of the compressor/expander can be increased by 21 timesover the case with uniform chamber shape, uniform porous medium distribution and uniform piston speed whilemaintaining overall efficiency of 92%. This leads to a 2nd stage (7-210 bar [0.7-21MPa] ) compression/expansiontime of 1.5s and a power density of 1.47MW/m

3 (does not include the intake portion of the cycle, which isnot limited by heat transfer). Figure 11 shows the optimal compression trajectory, porous medium distribution andchamber shape. The combined effect of introducing a porous medium and of optimizing the trajectory, distributionof porous medium and chamber shape is that power density has been increased by over 200 times, i.e. for a givenpower density and desired efficiency, the size of the compressor/expander chamber size has been reduced by 200times!

An issue with implementing the optimal trajectory is that it requires a large liquid piston pump/motor toaccommodate the fast segment of the trajectory, but it must also operate at low displacement for the slow segment.A possible approach to mitigating this issue is with the use of an intensifier [30].

C. Efficient power-takeoff via an adjustable linkage liquid piston pump/motor

The discussions above focus on the gas compression/expansion processes that take place in the compres-sion/expansion chamber. The hydraulic (water) pump/motor that provides the liquid piston flow must also be efficientand power-dense. This pump/motor is coupled to the hydraulic pump/motor and the synchronous AC generator.To meet the large variations in flow rate required for the optimal liquid piston trajectory, while operating at theconstant speed of the synchronous AC generator, the pump/motor displacement must be variable. The optimal

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Fig. 12. Diagram of the adjustable six-bar linkage of the VDLP.

trajectory requires that this pump/motor operates at low displacement and low pressure for a large portion ofthe liquid piston stroke, which is a region of low efficiency for most variable displacement pumps. Furthermore,most variable displacement pump architectures use the working fluid to lubricate the pump mechanism, creatingtribological, corrosion, and leakage challenges when pumping water. For these reasons, a new water hydraulicpump/motor architecture was developed specifically for controlling the liquid piston flow rate in the OA-ICAESsystem.

The new water pump architecture, the Variable Displacement Linkage Pump (VDLP), uses an adjustable six-bar linkage to drive the pistons. As seen in Fig. 12, the adjustable linkage is driven by an input crank that causesreciprocation of the piston through the kinematic constraints of the coupler link, connecting rod, and rocker link. Bymoving the adjustable ground pivot of the rocker link, the stroke length of the piston is varied. As the rocker link andconnecting rod are the same length, when the adjustable ground pivot becomes co-linear with the axis of the piston,there is no translation of the piston, resulting in zero pump displacement. In contrast to most variable displacementpump architectures where the unswept volume in the cylinder increases as the displacement decreases, the pistonin the VDLP reaches the same top-dead-center position regardless of the linkage displacement. This minimizes theunswept fluid volume and the associated compressible energy loss. There are four kinematic configurations thatachieve both constant top-dead-center and reach zero displacement, each with trade-offs regarding piston stroke,linkage footprint area, and transmission angles [31], [32].

An important metric of any pump is the flow ripple, the variation in the flow rate through a cycle. Excessive flowripple is detrimental in the liquid piston compressor as it increases the acceleration of the liquid piston, which canlead to water-air interface instability at operating frequencies lower than possible with a smooth flow rate. The firstway the flow ripple is minimized in the VDLP is through the use of multiple cylinders. The focus for the ICAESwork has been on a three-cylinder, inline pump design, where the crank throws are phase shifted 120 degrees (Fig.13) although other configurations, such as radial pistons have also been explored. Second, the design of the linklengths provides some control over the displacement trajectory of the pistons throughout the stroke. Designing thepump kinematics with consideration for the addition of the flow rate from the multiple cylinders, including effectsdue to fluid compressibility, allows the flow ripple to be significantly decreased.

The VDLP uses all pin joints, in contrast to the spherical and planar hydrostatic bearings found in axial pistonand other pump architectures, which are the largest source of energy loss [33]. Rolling element bearings are usedthroughout the linkage, including the main and crank pins on the split crankshaft. These bearings are all splashlubricated. The rotation of most of the joints in the linkage decreases as the displacement of the piston decreases,causing the mechanical energy loss to scale with output power. The low friction and scaling energy loss enable theadjustable linkage pump to have good mechanical efficiency across a wide displacement range.

The VDLP can operate with water and other non-lubricating fluids by preventing the pumped fluid from enteringthe pump case. The ceramic pistons use a high-pressure v-packing seal. Behind the high pressure seal is a drainport and a low-pressure wiper seal. The piston is supported by a crosshead bearing, which is splash lubricated from

13

Fig. 13. Three-cylinder inline VDLP

Fig. 14. Predicted efficiency of the optimized VDLP at 21MPa and 30Hz.

the pump linkage. The crosshead bearing not only centers the piston in the seal, but also reacts to radial loadsgenerated by the linkage. The positive piston seal and low unswept volume result in good volumetric efficiency.

To maximize the efficiency of the VDLP for the ICAES system, the pump parameters are optimized for thecompression/expansion cycle. For the optimization, a mathematical model was constructed of the dynamic behaviorof the pump and the primary energy loss mechanisms [32], [34]. The dynamic model accounts for the fluid inertiain the inlet and lines, the dynamics of the inlet and outlet valves, the pressure dynamics in the cylinder, the linkagedynamics, and the fluid dynamics in the manifold. The primary energy loss mechanisms are the friction in therolling-element bearings, viscous friction and leakage of the piston, throttling of flow across the inlet and outletvalves, and shaft seal friction. The model was validated on three different generations of prototypes, demonstratinggood agreement in terms of dynamic behavior and efficiency [35], [36]. For the optimized pump geometry, themodel predicts an efficiency of over 90% over all displacements above 10%, which is a significant improvementover typical axial piston pumps, as seen in Fig. 14.

IV. USING WATER DROPLET SPRAY TO ENHANCE HEAT TRANSFER

The liquid piston approach above has a significant disadvantage when compressing from, or expanding airto, atmospheric pressure. It is that a large liquid piston pump/motor is needed to provide the liquid flow rateequivalent to the air volume flow rate at atmospheric pressure. Such high flow, low pressure operating conditionsare ill suited for hydraulic pump/motors. Moreover, advantages of sealing, eliminating dead volume, and optimizingcompression/expansion are also less essential at low pressure. Thus, the liquid piston approach will be used for thehigh pressure stage, starting from 10 bar (1MPa). This reduces the required liquid flow rate and pump/motor sizeby 10 times!

14

Fig. 15. Concept of direct injection as a function of stroke angle.

For the low pressure (1-10bar [0.1-1MPa]) stage, a mechanical piston approach, running at high frequency (⇠20Hz), similar to a crank-shaft engine can be used. For heat transfer, minute water droplets are injected directly intothe chamber [10]. Water has a high heat capacity so a small amount (⇠ 1/1000 by volume) of water, if properlydistributed in the air space, can keep the process of air compression/expansion nearly isothermal. With smallersized droplets, the total surface area for heat transfer increases dramatically for a given mass fraction of water. Theheat transfer coefficient also increases as droplet size decreases due to the shrinking of the boundary layer. For 20µm, 50 µm and 100 µm droplets, the heat transfer coefficients are of the order 6000, 5000 and 3500Wm

�2K

�1,respectively! Similar to optimizing the compression/expansion trajectory, for a fixed amount of water to be sprayed,the trajectory of water sprays can also be optimized to maximize performance [17].

A schematic of the direct injection spray system is shown in Fig. 15. The compression chamber is orientedvertically to allow a liquid piston to be used in conjunction with spray. As the piston descends, direct injectioninitiates water spray with air suction simultaneously, so water droplets have filled the chamber when the suctionstroke finishes. As the piston ascends, and the compression stroke continues, water spray injection continues to keepthe chamber full of droplets, thereby maximizing heat transfer. When the air pressure reaches the prescribed valueof compression, the valve is opened to the next compression stage or to the accumulator tank, and the compressedair is pushed out of the compression chamber during the rest of the compression stroke. During expansion, thesame amount of heat transfer has to be supplied by droplets at ambient temperature again, to ensure expansionat a constant temperature. This way, the power used to run the compressor during the energy storage stage canideally be completely recovered during the energy re-generation stage. Such an isothermal process will have anideal efficiency of 100%. Note that the energy consumed by spraying is very small [10].

To determine the amount of water employed for cooling, the total spray mass is considered. The amount ofwater injected is defined by using total discharged spray mass in a single compression cycle. This injected masscan be expressed non-dimensionally in terms of the injected mass loading, defined as the ratio of water spray massdischarged (m

spray

) to the mass of dry air drawn into the piston chamber (ma

), i.e. ML = m

spray

/m

a

.The injected mass loading (ML) is based on the liquid flow rate of a given nozzle, the injection period, and the

compressed gas mass dependent on the intake pressure and the initial compression chamber volume. In addition,one may define the transient mass loading (ML

t

) based on the instantaneous spray mass aloft in the gas. Thisparameter is initially zero and increases during the spray injection period. If the droplet mass is never lost, onceinjected, ML

t

= ML at the end of spray injection. However, droplet losses caused by hitting the chamber wall orpiston surface will result in ML

t

< ML. These droplet losses may be counteracted by internal vortices that canhelp keep the droplets aloft in the gas for a longer time.

Theoretically, to determine overall efficiency, one may characterize the pressure rise as bounded between theisothermal and the adiabatic processes. During compression, one may define the polytropic index (n) as therelationship between pressure increase and volume decrease

P2

P1=

✓V1

V2

◆n

15

This index represents the overall performance of the compression with the lowest value being ideal. In the caseof isothermal compression (where work is used exclusively to increase pressure and no work is lost to internalenergy rise), the temperature is constant. As a result, the pressure is linearly proportional to density (and inverselyproportional to volume) during compression so that n is unity. This condition will result if there is high heat transferbetween the droplets and the gas. In the case of adiabatic compression, this index will equal the gas specific heatratio (�

g

= 1.4 for air). This condition will result in the least amount of work directed at pressure rise since somework is instead used to create temperature rise. For CAES, this work employed for temperature rise is consideredto be wasted, since it is lost to the ambient conditions when the compressed air is stored for longer periods.

The polytrophic index for the case of isothermal compression (minimum work requirement) can be obtained byconsidering infinitely small drops so that the heat transfer is infinitely fast. In this limit, the polytropic index canbe expressed in terms of the liquid spray mass loading and the specific heats of the droplets (c

d

) and of the gas(c

p

) as

n = �

g

1 +ML(cd

/c

p

)

1 + �

g

ML(cd

/c

p

)(4)

This expression represents the smallest possible polytropic index for a given droplet mass loading. When themass loading becomes infinite, the polytropic index trends to one, which indicates isothermal compression. Thus,theoretically, discharging a very large amount of liquid in small droplets (to promote fast heat transfer) helps toachieve near-isothermal compression. However, practically, it is difficult for a single nozzle to produce large massquantities while ensuring small droplets.

If pressure ratio and volume ratio are known for a certain compression process, the average polytropic index canbe calculated. However, the polytropic index for the actual compression process will vary with time depending onthe instantaneous heat transfer rate and the transient mass loading. The entire compression process can be discretizedinto a number of sub-processes, where polytropic indexes can be assumed to be constants for each discrete timeinterval.

The test conditions investigated are consistent for a single compression/expansion chamber with a geometrytypical of conventional piston cylinders. In particular, a cylinder compression chamber with an inner diameter of 15cm, a length of 30 cm, and a pressure ratio (initial value to final value) of 10 are employed. A single pressure-swirlnozzle orifice is located in the center of piston top wall. For spray discharge, pressure-swirl nozzles were found tobe most effective for liquid piston compression. Herein, the spray-cooling concept is investigated to achieve nearly-isothermal compression for a three-stage compression system. The compression ratios for the three stages are 10:1,7:1, and 5:1, based on ratios that are reasonable to achieve in terms of sealing and mechanical operation, andleading to a final pressure of 350 bar (35MPa). For fabrication simplicity, it can be desirable to set the dimensionsof the chambers in all three stages to be equal. Three different cases are considered to examine the operationalperformance by varying the intake/initial pressure and the spray mass injected. Case 1 is a first-stage cylinder withan initial air pressure of one atmosphere and the same nozzle conditions as [10], which corresponds to a totalinjected mass loading of 0.12. Case 2 is also a first-stage cylinder but the spray flow rate is adjusted to achievethe maximum experimental flow rate which allows droplets with the same mean diameter as Case 1, resulting inan injected mass loading of 1.6. Case 3 uses the same spray conditions as Case 2 but for a second-stage cylinderwith an initial air pressure of 9.6 atmospheres, which resulted in an injected mass loading of 0.185 (due to higherdensity and mass of air in the cylinder). Therefore, comparing Cases 1 and 2 allows the effect of mass loading tobe understood for a fixed initial pressure, while comparing Cases 2 and 3 allows the effect of initial pressure tobe understood for a fixed injected liquid mass. In addition, comparing Cases 1 and 3 allows the effect of initialpressure to be understood for a similar mass loading.

In the one-dimensional simulation [37], gas and liquid phase ordinary differential equations are integrated intime with a finite difference approach, while the two-dimensional simulation [38] employs an Eulerian numericalapproach for the gas phase and the Lagrangian approach for the liquid phase. To describe the influence of dropletheat transfer on compression thermodynamics, pressure-volume curves are shown in Fig. 16 (left). In order to makethe first- and second stage- curves to be comparable, a pressure ratio is used for the vertical axis. The results showthat injected mass loading is a primary indicator for compression performance for both 1D and 2D simulations.This is evident by comparing cases with similar mass loading but different spray conditions, whose P-V curvesare close to each other. For large mass loading, both 1D and 2D models show a substantial improvement tending

16

Fig. 16. Left: Pressure ratio vs. piston volume during compression. Right: Compression efficiency for different injected mass loading (ML)values. 1-D and 2-D indicate 1-D and 2-D computational procedures.

toward isothermal conditions as ML increases. Shown in Fig. 16 (right), all of the cases are compared with thetheoretical value, which assumes infinitely small drop sizes (for a given mass loading) so that droplet heat transferis immediate and assumes that the average mass loading is based on the total drop mass injected minus the mass ofdrops hitting the piston surface. For the ML=1.6 case, the efficiency is significantly higher than 90% for both 1Dand 2D results. The efficiency for this case is somewhat lower than the theoretical result, owing to droplet lossesand the thermal inertia of finite droplet diameters. In the lower mass loading cases, the 2D simulations actuallypredict higher efficiency than theory which can be explained by an over-prediction of droplet deposition on thewall surface. This is because of the vortex formed in the chamber, which tends to prevent droplet losses. Despitethese differences, it is interesting to note that the overall compression efficiency can be reasonably estimated bytheory, i.e. is primarily a function of mass loading for present conditions.

V. SYSTEMS AND CONTROL

Control systems are needed for the proposed OA-ICAES in Fig. 1 for proper operation. They are needed at theplant operation level, and at the supervisory control level.

The plant level controller in [7] uses the control inputs of 1) the displacement of the pump in the nacelle;2) the displacement of the down-tower pump/motor; and 3) the displacement of the near-isothermal air compres-sor/expander. The primary objectives are a) to optimize the wind energy capture above and below the cut-off windspeeds (the so-called regions 2 and 3), b) to fulfill the power demand (at the desired 60Hz frequency without usingpower electronics). Secondarily, the control system can also choose to maintain the open accumulator pressureclose to the nominal value (210 bar [21MPa]). Maximum wind energy capture requires controlling the wind turbinespeed according to the optimal tip speed ratio. By controlling the slip speed of the common shaft relative to thesynchronous speed of the generator, desired power/current output is satisfied. Excess or deficit power is made upby the energy storage either with the power-dense hydraulic power path for transient power or the energy-densepneumatic path for steady power.

As mentioned earlier, the open accumulator has two power paths - a hydraulic path and a pneumatic path, to storeenergy in or regenerate energy from the storage. The hydraulic path is power-dense whereas the pneumatic path isenergy-dense. The control system in [7] uses the hydraulic power path to accommodate high frequency, transientpower from the wind or from the demand; and the pneumatic path is used for low frequency steady power. Aninteresting consequence of this approach is that the open accumulator absorbs and filters the high frequency windgust directly without needing to actuate either the hydraulic or the pneumatic power paths. Figure 17 shows thisresult as well as the ability of the controller to optimize wind energy capture and to meet power demand. Noticethat pressure variation is less than one bar even as the accumulator is absorbing the high frequency wind powervariation.

A supervisory controller determines when the system should store or generate energy. In [39], a supervisorycontroller which does so in order to optimize the total revenue is developed. This controller takes into account

17

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 16001

2

3

4

5

6

7

8

9

10

1⃝a⃝ b⃝ c⃝

Win

d Sp

eed

(m/s

)

Wind

Desired Generator Power

Time (s) 0 200 400 600 800 1000 1200 1400 1600

0.2

0.6

1

Des

ired

Gen

erat

or P

ower

(MW

)

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600−2

−1.5

−1

−0.5

0

0.5

1

2⃝

Dow

n To

wer

P/M

Dis

p. (l

it/re

v)

Down TowerPump/Motor

Liquid Piston AirC/E Pump/Motor

Time (s) 0 200 400 600 800 1000 1200 1400 1600

−80

−60

−40

−20

0

20

40

Liq.

Pis

ton

Air

C/E

Dis

p. (l

it/re

v)0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600

199

200

201

3⃝

Air

Pres

sure

Rat

io

VolumePressure Ratio

Time (s) 0 200 400 600 800 1000 1200 1400 1600

658

659

660

661

662

663

664

665

666

Air

Volu

me

(m3 )

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 16000.15

0.3

0.45

0.6

0.75

0.9

1.05

4⃝

Gen

erat

or P

ower

(MW

)

Tip Speed Ratio

Generator Power

Time (s) 0 200 400 600 800 1000 1200 1400 1600

2

3

4

5

6

7

8

9

Tip

Spee

d R

atio

0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600−40

−20

0

20

40

5⃝

Liqu

id F

low

Rat

e (li

t/s)

Air Flow

Liquid Flow

Time (s) 0 200 400 600 800 1000 1200 1400 1600

−2.4

−1.8

−1.2

−0.6

0

0.6

1.2

1.8

2.4

Air

Mas

s Fl

ow R

ate

(Kg/

s)

Fig. 17. Sample results with a stochastic wind speed profile and step changes in power demand (taken from [7]).

18

Fig. 18. Sample supervisory control results for a two-week period in July.

components’ efficiency characteristics and, currently, assumes that the wind and electricity variations are known inadvance. Not surprising, the control tends to store energy when the electricity price is low, and generate energywhen the electricity price is high. Figure 18 shows a sample simulated control results using historical wind andelectricity price data. Here, the system is allowed to store energy from the grid when the electricity price is low.As expected the system generates energy when the electricity price is high and stores energy when it is low. TableII shows a sample comparison of the revenue and other operating statistics for the wind turbine in a one-weeksummer period under various scenarios.

For a typical summer week (when the price variation is large), the storage system increases the revenue by nearly140% when the system can buy and sell electricity to/from the grid despite the lower efficiency of the hydrauliccomponents compared to the gearbox system. It is also interesting to note that allowing the accumulator pressureto vary rather than be tightly regulated at the nominal pressure, tends to increase revenue by 10-15% and efficiencyby up to 4%. Notice that the revenue increase due to price arbitrage depends significantly on the price variation.During winter periods, the revenue increase is much less significant (⇠ 14%) [7], [39].

The supervisory controller has provided some important insight into both control and design. For example, welearn that it is advantageous for the open accumulator pressure to remain low (with limits) to increase systemefficiency. Also, by simulating the system with different accumulator volumes and compressor/expander powercapabilities, one can trade-off between size of the storage and the power capability to gain the same revenue.

VI. DISCUSSION

In this chapter, we have reviewed the concept of a novel compressed air energy storage (CAES) system that isfree of fossil fuel, not tied to geological restrictions, and is well suited when a power source in the mechanicaldomain is available. For this reason, we anticipate that wind turbines, especially off-shore wind turbines will beideal applications. However, as shown in the supervisory control results in Section V, the system can also beprofitably used for storing excess electricity. In this function, the system serves as a generic storage node on thegrid, such as at a substation.

It has often been said that electricity price arbitrage is the least valuable attribute of storage. As an operator,the ancillary control services for the grid, such as frequency regulation or grid stabilization can be much moreprofitable. Such services are now provided by the so called spinning reserves, which are basically rotating inertias

19

TABLE IIENERGY CAPTURED, EFFICIENCY AND REVENUES FOR A 1.5 MW WIND TURBINE OVER TWO 7-DAY PERIODS JULY, 2012.

Windcaptured(MWh)

Electricitysold(MWh)

Efficiency(%)

Revenue ($)/%increase overcase 1

Conventional wind turbine 30.1 25.7 85.5 $1570Hydrostatic wind turbine w/no storage 30.1 20.7 68.5 $1268/-19.3%Proposed system w/3.6 MWh storage(sell, constant pressure)

30.1 18.7 62 $2068/+31.7%

Proposed system w/3.6 MWh storage(sell/buy, constant pressure)

30.1 36.3 64.6 $2801/+78.3%

Proposed system w/3.6 MWh storage(sell, varying pressure)

30.1 20.3 66.8 $2353.8/+49.9%

Proposed system w/3.6 MWh storage(sell/buy, varying pressure)

30.1 49.7 68.4 $3737/+137.9%

that can respond instantaneously to provide or absorb power mechanically. The proposed OA-ICAES system iswell positioned to provide these for two reasons: 1) it preserves the synchronous machine in the system that has aphysical rotating inertia; 2) extra energy can be provided or absorbed by the storage system through the actuation ofthe hydraulic power path. Hydraulic actuation typically has high control bandwidth since only a small mass needsto be actuated to control displacements. These physical attributes, together with a control system that can tightlyregulate the speed of the synchronous machine, can create a virtual spinning reserve that is as fast as a physicalinertia but can absorb/provide nearly unlimited amount of energy. By controlling the synchronous machine speed,the local frequency at the storage node can be regulated. An intriguing possibility is to see if more can be doneby coordinating with the rest of the grid, to help stabilize the rest of grid. More research is needed regarding thesepossibilities.

The performance of the near-isothermal compressor/expander is critical for the AO-ICAES system. In this chapter,we focus mostly on the heat transfer challenges since they limit the trade-off between power density and efficiency.However, there are other aspects that also need attention. We briefly discuss two of these below.

One aspect is the mass transfer processes between the water and air in the system, since air and water share thesame volume, both inside the compression/expansion chamber (with either liquid piston or water spray concepts)and also in the storage vessel. Inside the compressor, having air dissolved into the water or trapped by water filmsprevents that compressed air from being stored in the storage tank. Thus, it represents work that went into the aircompressor without the benefit of storing the resulting compressed air. A computation of this process can be foundin [40]. On the other hand, evaporation of water and condensation of steam from and to tiny droplets inside thecompression/expansion chamber may enhance heat transfer and hence the performance of the compressor/expander.Preliminary results indicate that for high efficiency operation when the compressed air temperature is kept low, theeffect of such phase change is not significant [41]. Inside the storage vessel of the open accumulator, high pressureair can also dissolve into the water as governed by Henry’s Law. At 200 bar (20 MPa), 3.7 g of air is dissolved in1 kg of water. This contains 1.5 kJ of energy or 7.7% of the hydraulic energy. To recuperate this energy, care isneeded in the design and operation of the hydraulic motor connected to the liquid port of the storage vessel. Theenergy in the dissolved compressed air can be retrieved by controlling the valve timing of the hydraulic motor suchthat the air is released from solution and then allowed to fully expand. Recent work on so called digital hydraulicsusing active valvings would be applicable to this end [42], [43].

Another aspect that needs attention is the propensity for air and water to be trapped inside the porous matrix.During compression, trapped air contributes to increased dead volume and lost work since the compressed airbubbles consume work but do not end up in the storage vessel. Similarly, during expansion, trapped air initially atlow pressure is compressed by compressed air from storage, thus reducing work output and efficiency. Incompletewater drainage, on the other hand, reduces the volume for fresh air intake, thus reducing the effective displacementof the compressor. Water that remains can likely bridge the porous medium cells trapping air within the matrix.Without treatment, water hold- up in the ABS interrupted plate heat exchangers can be as much as 80% of the dryweight of the exchangers. To solve this problem, processes for applying durable nano-textured coatings that makethe surfaces super-hydrophobic have been developed [44]. With such coatings, water holdup is decreased by 8-fold

20

at ambient pressure. Further work is needed to ensure proper water drainage and to prevent air trapping duringhigh pressure operation in the compressor/expander.

The CAES system described in this chapter is based upon near-isothermal compression/expansion. In our analysis,a conservative assumption is made that the compressed air returns to ambient temperature in the storage before it isexpanded for regeneration. If the storage vessels can be kept warm, either through insulation or by heating (e.g. viasolar or waste heat), energy output will increase. Taken to the extreme, when the compressed air can be reheatedbefore expansion, to the temperature at the exit of the compression phase, the process resembles the approachesof advanced adiabatic CAES [45] and thermal energy storage (TES). It should be noted, however, design trade-offbetween the isothermal and adiabatic regimes are quite different. For example, for effective TES, a high temperaturemust be attained and heat should not escape during the compression process itself. This is in contrast to isothermalCAES where temperature should be kept low and heat transfer during compression is desirable.

VII. CONCLUSIONS

In this chapter, an open accumulator isothermal compressed air energy storage system (OA-ICAES) is described.The open accumulator architecture offers high energy density, high transient power density, and fast response;whereas the isothermal compressor/expander offers improved efficiency and power density. It can be coupled witha wind-turbine to provide predictable and on-demand renewable energy, and to regulate grid frequency. The systemcan be sited anywhere (unlike pumped hydro) and does not need fossil fuel (unlike existing, conventional CAES).Its competitive advantages over various electrical batteries are significantly lower cost, higher reliability, higherpower density, greater longevity, and unlimited charge/recharge cycles.

To realize this concept, the isothermal compressor/expander with augmented heat transfer capability (via the liquidpiston with porous media and spray cooling/warming concepts) and efficient power takeoff (PTO) was developed.Optimization of the trajectory, porous medium distribution and compressor/expander chamber shape have a dramaticeffect on the efficiency-power density trade-off. Control systems that operate at the plant and at the supervisorylevel have also been developed to enable the best system performance.

By offering a cost-effective and efficient grid-scale energy storage concept, larger amount of renewable resourcescan be better and more reliably integrated into the electrical grid.

ACKNOWLEDGEMENT

This work is supported by the National Science Foundation under Grant EFRI 1038294 and the Institute forRenewable Energy and Environments (IREE) at the University of Minnesota under Grant RM-0027-11. Many post-doctoral and graduate student researchers contributed greatly to this work, in particular, Dr. Mohsen Saadat, Dr.Farzad Shirazi, Mr. Jacob Wieberdink, Dr. Shawn Willheim, Mr. Bo Yan and Dr. Chao Zhang.

REFERENCES

[1] D. Spera, Wind Turbine Technology - Fundamental Concepts of Wind Turbing Engineering, 2nd ed., ASME Press, 2009.[2] J. Green, A. Bowen, L. Fingersh and Y. Wan, ”Electrical Collection and Transmission for Offshore Wind Power,” National Renewable

Energy Laboratory (NREL) , CO, 2007.[3] W. Musial and S. Butterfield, ”Future for Offshore Wind Energy in the United States,” National Renewable Energy Laboratory (NREL),

CO.[4] R. Carnegie, D. Gothan, D. Nderitu and P. Preckel, ”Utility Scale Energy Storage Systems - Benefits, Applications and Technologies,”

2013.[5] B. Elmegaard and W. Brix, ”Efficiency of compressed air energy storage,” in The 24th International Conference on Efficiency, Cost,

Optimization, Simulation and Environmental Impact of Energy Systems, 2011.[6] Li, P., Loth, E., Simon, T., Van de Ven, J., and Crane, S., “Compressed Air Energy Storage for Offshore Wind Turbines,” Presented at

the IFPE (International Fluid Power Exposition) March 22-26, 2011, Las Vegas, NV.[7] M. Saadat and P. Y. Li, ”Modeling and Control of an Open Accumulator Compressed Air Energy Storage (CAES) System for Wind

Turbines,” Applied Energy, vol. 137, pp. 603-616, January 2015.[8] J. D. Van de Ven and P. Y. Li, ”Liquid Piston Gas Compression,” Applied Energy, vol. 86, no. 10, pp. 2183-2191, October 2009.[9] C. Zhang, J. Wieberdink, F. Shirazi, B. Yan, T. Simon and P. Y. Li, ”Numerical investigation of metal-foam filled liquid piston

compressor using a two-energy equation formulation based on experimentally validated models,” in ASME-IMECE, San Diego, 2013.[10] C. Qin, E. Loth, P. Y. Li, T. Simon and J. Van de Ven, ”Spray cooling concept for wind based compressed air energy storage,” Journal

of renewable and sustainable energy, vol. 6, no. 4, p. #0423125, 2014.[11] P. Y. Li, J. D. Van de Ven and C. Sancken, ”Open accumulator concept for compact fluid power energy storage,” in Proceedings of

the 2007 ASME-IMECE, Seattle, 2007.

21

[12] J. Wieberdink, ”Increasing Efficiency and Power Density of a Liquid Piston Air Compressor/Expander With Porous Media Heat TransferElements.,” M.S. Thesis, Department of Mechanical Engineering, University of Minnesota, 2014.

[13] C. Sancken and P. Y. Li, ”Optimal efficiency-power relationship for an air motor-compressor in an energy storage and regenerationsystem,” in ASME Dynamic Systems Control Conference / Bath Fluid Power and Motion Control Symposium, Hollywood, CA, 2009.

[14] A. T. Rice and P. Y. Li, ”Optimal Efficiency-Power Tradeoff for an air motor/compressor with volume varying heat transfer capabilities,”in ASME Dynamic Systems and Control Conference, Arlington, VA, 2011.

[15] M. Saadat, P. Y. Li and T. W. Simon, ”Optimal trajectories for a liquid piston compressor/expander in a compressed air energy storagesystem with consideration of heat transfer and friction,” in American Control Conference, Montreal, Canada, 2012.

[16] M. Saadat and P. Y. Li, ”Combined optimal design and control of a near-isothermal air compressor/expander for a CAES sysem forwind turbine,” in ASME Dynamic Systems and Control Conference, Columbus, OH, 2015.

[17] M. Saadat, F. Shirazi and P. Y. Li, ”Optimal Trajectories of Water Spray for a Liquid Piston Air Compressor”, ASME 2013 SummerHeat Transfer Conference HT2013-17611, Minneapolis, MN, July 2013.

[18] C. Zhang, F. Shirazi, B. Yan, T. Simon, P. Li, J. Van de Ven, “Design of an Interrupted-Plate Heat Exchanger Used in a Liquid-PistonCompression Chamber for Compressed Air Energy Storage,” HT2013-17484, ASME Summer Heat Transfer Conference, Minneapolis,MN. 2013

[19] C. Zhang, T.W. Simon, P.Y. Li, and J. Van de Ven, ”Numerical Modeling of Three Dimensional Heat Transfer and fluid Flow throughInterrupted Plates using Unit Cell Scale,” Journal of Porous Media, 6 (2): 145–158 (2015), and Proceedings of the 15th InternationalHeat Transfer Conference, IHTC-15, August 10-15, 2014, Kyoto, Japan.

[20] C. Zhang, T.W. Simon, P. Li, “Optimization of the Axial Porosity Distribution of Porous Inserts in a Liquid Piston Gas Compressorusing a One-Dimensional Formulation,” IMECE2013-63862, 2013 IMECE conference, San Diego, CA. 2013.

[21] C. Zhang, B. Yan, J. Wieberdink, P. Li, J. D. Van de Ven, and T. W. Simon, ”Thermal Analysis of a Compressor for Application toCompressed Air Energy Storage,” IWHT2013-001, Proceedings of IWHT2013 2nd International Workshop on Heat Transfer Advancesfor Energy Conservation and Pollution Control October 18-21, 2013, Xi’an, China 2013.

[22] F. Shirazi, M. Saadat, B. Yan, P. Y. Li and T. Simon, ”Optimal Control Experimentation of Compression Trajectories for a LiquidPiston Air Compressor,” in ASME 2013 Summer Heat Transfer Conference, HT2013-17613, Minneapolis, MN, 2013.

[23] F. Shirazi, M. Saadat, B. Yan, P. Li, T. Simon, ”Iterative Optimal and Adaptive Control of a Near Isothermal Liquid Piston AirCompressor in a Compressed Air Energy Storage System,” 2013 ACC IEEE Control Systems Society Conference, Paper No. 1702,2013 American Control Conference, Washington, DC, 2013.

[24] C. Zhang, T.W. Simon, J. Wieberdink, P.Y. Li, J.D. Van de Ven, and E. Loth, “Numerical Analysis of Heat Exchangers used in a LiquidPiston Compressor using a One-Dimensional Model with an Embedded Two-Dimensional Sub-model,” IMECE2014-38567, ASME2014 International Mechanical Engineering Congress and Exposition, November 14-20, Montreal, Canada, 2014.

[25] C. Zhang, T. W. Simon and P. Y. Li, “Storage Power and Efficiency Analysis Based on CFD for Air Compressors used for CompressedAir Energy Storage,” IMECE2012-88985, Houston, TX, 2012.

[26] C. Zhang, “CFD Simulations and Thermal Design for Application to Compressed Air Energy Storage,” Ph.D. Thesis, MechanicalEngineering Department, University of Minnesota, 2015.

[27] C. Zhang, J. Wieberdink, F. Shirazi, B. Yan, T. W. Simon, P. Y. Li, “Numerical Investigation of Metal-Foam Filled Liquid PistonCompressor Using a Two-Energy Equation Formulation Based on Experimentally Validated Models,” IMECE2013-63854, 2013 IMECEconference, San Diego, CA, 2013.

[28] B. Yan, J. Wieberdink, F. Shirazi, P. Y. Li, T. W. Simon and J. D. Van de Ven, ”Experimental Study of Heat Transfer Enhancement ina Liquid Piston Compressor/Expander using Porous Media Inserts,” Applied Energy, vol. 154, no. Sept., pp. 40-50, 2015.

[29] M. Saadat, A. Srivatsa, P. Y. Li and T. W. Simon, “Air Compression Performance Improvement Via Trajecotry Optimization -Experimental Validation,” 2016 ASME Dynamic Systems and Control Conference, Minneapolis, Minnesota, #9825, 2016.

[30] P. Y. Li and M. Saadat, ”An approach to reduce the flow requirement for a liquid piston air compressor/expander in a compressed airenergy storage (CAES) system”, 2nd Offshore Energy and Storage Symposium (OSES), Edinburgh, U.K., July 2015.

[31] S. Wilhelm and J. Van de Ven, ”Synthesis of a Variable Displacement Linkage for a Hydraulic Transformer,” ASME InternationalDesign Engineering Technical Conference, Washington, D.C., 2011.

[32] S. Wilhelm and J. D. Van de Ven, ”Design and Testing of an Adjustable Linkage for a Variable Displacement Pump,” Journal ofMechanisms and Robotics, 5(4), p. 041008, 2013.

[33] J. Ivantysyn, and M. Ivantysynova, 2001, Hydrostatic Pumps and Motors: Principles, Design, Performance, Modelling, Analysis, Controland Testing, Tech Books International, New Dehli, India.

[34] S. Wilhelm, and J. D. Van de Ven, ”Design of a Variable Displacement Triplex Pump,” National Conference on Fluid Power, InternationalFluid Power Exposition, Las Vegas, NV, 2014.

[35] S. Wilhelm, and J.D. Van de Ven, ”Efficiency Testing of an Adjustable Linkage Triplex Pump,” ASME/BATH 2014 Symposium onFluid Power & Motion Control, Bath, United Kingdom, pp. FPMC2014-7856, 2014.

[36] S. Wilhelm, and J.D. Van de Ven, ”Adjustable Linkage Pump: Efficiency Modeling and Experimental Validation,” Journal of Mechanismsand Robotics, 7(3), 2015.

[37] C. Qin, and E. Loth. ”Liquid piston compression efficiency with droplet heat transfer.” Applied Energy 114 (2014): 539-550.[38] C. Qin, and E. Loth. ”Simulation of spray direct injection for compressed air energy storage.” Applied Thermal Engineering 95 (2016):

24-34.[39] M. Saadat and P. Y. Li, ”Revenue maximization of electricity generation for a wind turbine integrated with a compressed air energy

storage system,” in Proceedings of the 2014 American Control Conference, Portland, OR, 2014.[40] L. Huang, T. Simon, P. Y. Li and E. J. Hummelt, ”Analysis of dissolved gas in the application of liquid piston gas compression,” in

1st Thermal and Fluid Engineering Summer Conference, TFESC, August 9-12, 2015, New York City, USA, TFESC-12869[41] A. Srivatsa and P. Y. Li, “The effect of moisture on the efficiency and power density of a liquid piston air compressor/expander”, 2016

ASME Dynamic Systems and Control Conference, Paper-#9957, Minneapolis, Minnesota. October 2016.

22

[42] M. Linjama, “Digital Fluid Power - State of the Art,” Twelfth Scandinavian International Conference on Fluid Power, Tampere, Finland,2011.

[43] M. Ehsan, W. Rampen, W., and S. Salter, “Modeling of Digital-Displacement Pump-Motors and Their Application as Hydraulic Drivesfor Nonuniform Loads,” ASME Journal of Dynamic Systems Measurement and Control, Vol. 122, pp. 210-215, 2000.

[44] A. Milionis, K. Dang, M. Prato and E. Loth, “Liquid Repellent Nanocomposites Obtained from One-Step Water-Based Spray” Journalof Materials Chemistry A, 2015.

[45] F. de Samaniego Steta, “Modeling of an Advanced Adiabatic Compressed Air Energy Storage (AA-CAES) Unit and an OptimalModel-based Operation Strategy for its Integration into Power Markets”, M.S. Thesis, ETH, Zurich, October, 2010.